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The total energy of electron in the ground stateof hydrogen atom is – 13.6 eV. The kinetic energyof an electron in the first excited state is        [2007]
  • a)
    6.8 eV
  • b)
    13.6 eV
  • c)
    1.7 eV
  • d)
    3.4 eV.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The total energy of electron in the ground stateof hydrogen atom is &n...
Energy in the first excited state
But K.E. = –(Total energy) = +3.4 eV.
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The total energy of electron in the ground stateof hydrogen atom is &n...

Explanation:

The total energy of an electron in the ground state of a hydrogen atom is given as -13.6 eV. This energy is a combination of the potential energy and kinetic energy of the electron.

Kinetic Energy in the Ground State:
- In the ground state, the electron has the maximum negative energy of -13.6 eV.
- This negative energy indicates that the electron is bound to the nucleus.

Kinetic Energy in the First Excited State:
- When the electron is excited to the first excited state, it moves to a higher energy level.
- In the first excited state, the electron has a total energy greater than in the ground state.
- This means that the kinetic energy of the electron in the first excited state is higher than in the ground state.

Calculation:
- The increase in energy from the ground state to the first excited state is 13.6 eV.
- The kinetic energy of the electron in the first excited state is half of this increase in energy, as the potential energy also contributes.
- Therefore, the kinetic energy in the first excited state is 13.6 eV / 2 = 6.8 eV.

Therefore, the correct answer is option D) 3.4 eV.
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The total energy of electron in the ground stateof hydrogen atom is – 13.6 eV. The kinetic energyof an electron in the first excited state is [2007]a)6.8 eVb)13.6 eVc)1.7 eVd)3.4 eV.Correct answer is option 'D'. Can you explain this answer?
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